Mixtral 8x7B on 5.NF.A.1
Common Core Standard 5.NF.A.1
This standard covers the following:
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Problem: John has been learning to add and subtract fractions at school. He was given a problem during his homework that puzzled him. He had to take the sum of 48/56 and 95/23 and then subtract 34/26 from the result. What was the value that John found for this operation? Answer in simplest form.
Mixtral 8x7B:
Reasoning: First, we need to add 48/56 and 95/23. To do this, we need to find a common denominator, which is
Expected answer: 7702/2093
Correct? No
Problem: First, add the fractions 88/9 and 28/65. Then subtract the fraction 18/37 from the result. What is the result expressed as a simple fraction?
Mixtral 8x7B:
First, find the common denominator of 9 and 65, which is 585. 88/9 becomes (88 \* 65) / 585 = 5720 / 585 28/65 becomes (28 \* 9) / 585 = 252 / 585 Now add the fractions: 5720 / 585 + 252 / 585 = 5972 / 585 Now subtract 18/37 from the result: 5972 / 585 - (18 \* 16) / (37 \* 16) = 5972 / 585 - 288 / 592 The common denominator of 585 and 592 is 35520. 5972 / 585 becomes (5972 \* 60) / 35520 = 358320 / 35520 592 / 585 becomes (592 \* 60) / 35520 = 35520 / 35520 288 / 592 becomes (288 \* 60) / 35520 = 17280 / 35520 Now subtract: 358320 / 35520 - 17280 / 35520 = 341040 / 35520 Simplify the fraction: 341040 / 35520 = 34104 / 3552 = 8526 / 888 = 4263 / 444 = 1421 / 148 ### Answer: The result expressed as a simple fraction is 1421/148.
Expected answer: 210434/21645
Correct? No
Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?
Mixtral 8x7B:
Reasoning: First, we simplify 63/41 to the lowest terms, which is already in the lowest terms since 63 and 41 are both prime numbers. Next, we simplify 44/50 to the lowest terms by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 44/4 = 11 and 50/4 = 12.5, so 44/50 simplifies to 11/12.5. Now, we can add the two simplified fractions: 63/41 + 11/12.5. To add fractions, we need to have the same denominator, so we convert 63/41 to have a denominator of 12.5 by multiplying both the numerator and the denominator by 12.5/41: (63/41)*(12.5/12.5) = 19.6875/12.5. Now, we can add the two fractions: 19.6875/12.5 + 11/12.5 = (19.6875 + 11)/12.5 = 30.6875/12.5. The fraction 30.6875/12.5 cannot be simplified further, so this is the final answer. ### Answer: 30.6875/12.5 or approximately 2.455 when expressed as a decimal.
Expected answer: 2477/1025
Correct? No
Problem: John had 71/41 of a cake left and Emily added 41/77 of another cake to it. How much cake is there in total? Give your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to find a common denominator for the fractions 71/41 and 41/77. The least common multiple of 41 and 77 is 3307. 71/41 * (3307/3307) = 239/3307 41/77 * (41/41) = 168/3307 Now, we add the two fractions: 239/3307 + 168/3307 = 407/3307 Simplifying the fraction: 407/3307 is already in its simplest form. ### Answer: 407/3307
Expected answer: 7148/3157
Correct? No
Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.
Mixtral 8x7B:
First, find a common denominator for 65 and 35. The least common multiple of 65 and 35 is 260, so convert both fractions to have this common denominator. 10/65 becomes (10*4)/260 = 40/260, which simplifies to 2/13. 56/35 becomes (56*8)/260 = 448/260, which simplifies to 12/5. Now add the two simplified fractions: 2/13 + 12/5 = (2*5)/(13*5) + (12*13)/(5*13) = 10/65 + 156/65 = 166/65. This fraction does not simplify, so the final answer is 166/65. ### Answer: 166/65
Expected answer: 114/65
Correct? No
Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 81 and 47 is 3798. So, we convert the fractions to have this common denominator: 75/81 = (75 \* 47) / 81 = 3525 / 3798 97/47 = (97 \* 81) / 47 = 7809 / 3798 Then, we add the fractions: 3525 / 3798 + 7809 / 3798 = (3525 + 7809) / 3798 = 11334 / 3798 ### Answer: 11334/3798
Expected answer: 3794/1269
Correct? No
Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To subtract the fractions, we need to find a common denominator. The least common multiple of 1 and 53 is 53. 88/1 - (38/53)\*1 = 88/1 - 38/53 = (88\*53 - 38)/53 = 4644/53 However, the problem asks for the answer as a simplified fraction. The greatest common divisor of 4644 and 53 is 1, so the fraction is already in its simplest form. ### Answer: 4644/53
Expected answer: 4626/53
Correct? No
Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?
Mixtral 8x7B:
Reasoning: First, we perform the division operations: (0.851063829787234 + 1.3220338983050847) Then, we add the results: 2.1730977280923187 ### Answer: 2.1730977280923187 or approximately 2.17 (when rounded to two decimal places)
Expected answer: 6026/2773
Correct? No
Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need a common denominator. The least common multiple of 56 and 50 is 280. 89/56 = (89 \* 5)/(56 \* 5) = 445/280 48/50 = (48 \* 6)/(50 \* 6) = 288/300 Now, we can add the fractions: 445/280 + 288/300 = (445 \* 300 + 288 \* 280)/(280 \* 300) = 133650/84000 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 133650 and 84000 is 1050. So, 133650/84000 = (133650/1050)/(84000/1050) = 127/76 ### Answer: 127/76
Expected answer: 3569/1400
Correct? No
Problem: What is the result when you subtract 38/87 from the sum of 96/11 and 12/5? Please leave your answer as a fraction.
Mixtral 8x7B:
Reasoning: First, we need to find the sum of 96/11 and 12/5. To do this, we need a common denominator, which is 55 in this case. 96/11 + 12/5 = 96/11 + 24/55 = 88/55 + 24/55 = 112/55 Then, we subtract 38/87 from 112/55. To do this, we need a common denominator, which is 48990 in this case. 112/55 - 38/87 = 24480/48990 - 16860/48990 = 7620/48990 Simplifying the fraction, we get: 7620/48990 = 1524/9798 = 762/4899 ### Answer: 762/4899
Expected answer: 51154/4785
Correct? No
Problem: If you have a number that's 82 divided by 9 and from this you subtract 82 divided by 63, what's the resulting value? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: 82/9 - 82/63 = 82(63-18)/(9*63) = 82*45/567 = 1680/567 = 20/67 (simplified). ### Answer: 20/67
Expected answer: 164/21
Correct? No
Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.
Mixtral 8x7B:
Reasoning: First, we need to calculate the sum of 80/91 and 26/24. The least common multiple of 91 and 24 is 2184. So, we convert 80/91 to 1840/2184 and 26/24 to 624/2184. Then, we add them: 1840/2184 + 624/2184 = 2464/2184. Next, we subtract 2464/2184 from 23/3: 23/3 - 2464/218
Expected answer: 6229/1092
Correct? No
Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?
Mixtral 8x7B:
Reasoning: First, we need to convert each fraction to have the same denominator. The least common multiple of 18 and 60 is 180, so: 37/1
Expected answer: 221/90
Correct? No
Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 33/41 and 95/62, we need to find a common denominator. The least common multiple of 41 and 62 is 1682. So, we convert 33/41 to 33 \* 41/1682 = 1383/1682 and 95/62 to 95 \* 27/1682 = 2565/1682. Then, we add the two fractions: 1383/1682 + 2565/1682 = (1383 + 2565)/1682 = 3948/1682. Finally, we simplify the fraction: 3948/1682 = 18/7. ### Answer: 18/7
Expected answer: 5941/2542
Correct? No
Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to calculate the values inside the parentheses: (30 / 11) + (72 / 38) = (30 \* 38) / (11 \* 38) + (72 \* 11) / (38 \* 11) = 1140 / 418 + 792 / 418 = 1932 / 418 Now, we need to add this result to (81 / 34): (1932 / 418) + (81 / 34) = (1932 \* 34) / (418 \* 34) + (81 \* 418) / (34 \* 418) = 66084 / 14212 + 33658 / 14212 = 99742 / 14212 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator: GCD(99742, 14212) = 14 Now, we divide both the numerator and the denominator by the GCD: 99742 / 14 = 7124.43 and 14212 / 14 = 1015.14 Since the result is not a whole number, the fraction cannot be simplified further. ### Answer: 99742 / 14212
Expected answer: 49773/7106
Correct? No
Problem: What is the result of adding (64 / 34) + (3 / 24) and then adding the result to (41 / 96)? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to calculate the sum of (64 / 34) and (3 / 24). To do this, we need to find a common denominator for 34 and 24. The least common multiple of 34 and 24 is 15048. (64 / 34) can be written as (64 * 451) / 15048 = 2896 / 15048 (3 / 24) can be written as (3 * 625) / 15048 = 1875 / 15048 So, (64 / 34) + (3 / 24) = 2896 / 15048 + 1875 / 15048 = 4771 / 15048 Now, we need to add the result to (41 / 96). To do this, we need to find a common denominator for 15048 and 96. The least common multiple of 15048 and 96 is 15048. (4771 / 15048) can be written as (4771 / 15048) (41 / 96) can be written as (41 * 156) / 15048 = 6376 / 15048 So, (4771 / 15048) + (41 / 96) = 4771 / 15048 + 6376 / 15048 = 11147 / 15048 The simplified fraction of (64 / 34) + (3 / 24) + (41 / 96) is (11147 / 15048). ### Answer: 11147 / 15048
Expected answer: 3973/1632
Correct? No
Problem: Daniel has to solve a math problem for his homework that includes fractions. Initially, he has been asked to add 83/73 and 53/77. The result of this step he saved as 'w'. Then, he needs to add 80/76 to the result 'w'. How would he calculate the final answer in simplified fraction form?
Mixtral 8x7B:
Reasoning: First, Daniel needs to add the fractions 83/73 and 53/77. To do this, he needs to find a common denominator, which is 73 \* 77 = <<73*77=5621>>5621. So, 83/73 = (83 \* 77) / 5621 = 6401/5621 and 53/77 = (53 \* 73) / 5621 = 3889/5621. Now, he can add these two fractions: w = 6401/5621 + 3889/5621 = 10290/5621. Next, Daniel needs to add 80/76 to the result w. To do this, he needs to find a common denominator, which is 76 \* 5621 = <<76*5621=425996>>425996. So, w = 10290/5621 = (10290 \* 76) / 425996 = 783640/425996 and 80/76 = (80 \* 5621) / 425996 = 450080/425996. Now, he can add these two fractions: final answer = 783640/425996 + 450080/425996 = 1233720/425996, which simplifies to 1233720/425996 = 10/3. ### Answer: 10/3
Expected answer: 307360/106799
Correct? No
Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to get them over a common denominator. The least common multiple of 20 and 66 is 220, so we convert both fractions to have this denominator: 27/20 = (27 \* 11) / 220 = 297 / 220 14/66 = (14 \* 10) / 220 = 140 / 220 Now we can add the fractions: 297/220 + 140/220 = (297 + 140) / 220 = 437 / 220 Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7: 437 / 7 = 62.43, 220 / 7 = 31.43 ### Answer: 62/31 or 2 1/31 (when expressed as a mixed number)
Expected answer: 1031/660
Correct? No
Problem: What is the result of the expression ((32 / 14) - (22 / 47))? Write your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we perform the division operations: (32 / 14) = 16/7 and (22 / 47) = 22/47 Then, we subtract the two results: 16/7 - 22/47 = (16 \* 47 - 22 \* 7) / (7 \* 47) = 752/329 ### Answer: 752/329
Expected answer: 598/329
Correct? No
Problem: What is the sum of 74/61 and 41/53 expressed in fractions?
Mixtral 8x7B:
Reasoning: To find the sum of two fractions, we need to find a common denominator. The least common multiple (LCM) of 61 and 53 is 3253. The common denominator of 74/61 and 41/53 is therefore 3253. 74/61 = (74 \* 53) / 3253 = 3902/3253 41/53 = (41 \* 61) / 325
Expected answer: 6423/3233
Correct? No
Problem: First, find out the result of 94 / 2 - 74 / 57. Then add the result to 56 / 97. What fraction do you get?
Mixtral 8x7B:
Reasoning: First, perform the division operations: 94 / 2 = 47 74 / 57 ≈ 1.3 Then, subtract the second result from the first: 47 - 1.3 = 45.7 Next, perform the division operation: 56 / 97 ≈ 0.577 Finally, add the third result to the fourth: 45.7 + 0.577 = 46.277 So, the fraction is 46.277/1. ### Answer: 46.277
Expected answer: 255877/5529
Correct? No
Problem: What is the sum of 14/89 and the sum of 24/34 and 44/87? Give your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to find the sum of 24/34 and 44/87. To do this, find a common denominator (in this case, 34*87=2958) and rewrite the fractions with this common denominator. 24/34 + 44/87 = (24*87)/2958 + (44*34)/2958 = 2088/2958 + 1496/2958 = 3584/2958. Now, we need to find the sum of 14/89 and 3584/2958. To do this, find a common denominator (in this case, 89*2958=264262) and rewrite the fractions with this common denominator. 14/89 + 3584/2958 = (14*2958)/264262 + (3584*89)/264262 = 41412/264262 + 318176/264262 = 359588/264262. The fraction 359588/264262 cannot be simplified further. ### Answer: 359588/264262
Expected answer: 180194/131631
Correct? No
Problem: What would you get if you add 73/30 to 8/60?
Mixtral 8x7B:
Reasoning: To add the fractions 73/30 and 8/60, we need to get them to have a common denominator. The least common multiple of 30 and 60 is 60, so we convert 73/30 to 73*2/30*2 = 146/60 and 8/60 to 8*1/60*1 = 8/60. Then, we add the fractions: 146/60 + 8/60 = (146+8)/60 = 154/60. We can simplify this fraction to 77/30. ### Answer: 77/30
Expected answer: 77/30
Correct? Yes
Problem: If you take the result of adding 73/30 to 8/60 and then add it to itself again, what fraction do you get?
Mixtral 8x7B:
Reasoning: We found in the previous question that the sum of 73/30 and 8/60 is 154/60, which can be simplified to 77/30. To find the sum of this fraction and itself, we simply multiply the fraction by 2: 77/30 \* 2 = 154/30, which can be simplified to 51.33333333333/10. ### Answer: 51.33333333333/10 or 51 1/3 (when rounded to the nearest whole number)
Expected answer: 77/15
Correct? No
Problem: Suppose you originally had a fraction of 73/30. Now, instead of adding 8/60 to it, you decide to add 49/60. What fraction will you get in this case?
Mixtral 8x7B:
Reasoning: To add the fractions 73/30 and 49/60, we need to get them to have a common denominator. The least common multiple of 30 and 60 is 60, so we convert 73/30 to 73*2/30*2 = 146/60. Then, we add the fractions: 146/60 + 49/60 = (146+49)/60 = 195/60. We can simplify this fraction to 39/12 or 3 3/4. ### Answer: 3 3/4 or 39/12 (Note: The answer can be expressed as a mixed number or an improper fraction)
Expected answer: 13/4
Correct? No
Problem: Suppose you have the following three fractions: 82/49, 45/60, and 99/59. If you add the first fraction (82/49) with the second one (45/60), call this result 'd'. Then, add 'd' to the third fraction (99/59). What would be the resulting sum? Please provide your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to find the common denominator of 49 and 60, which is 2340. Then, convert 82/49 to 1796/2340 and 45/60 to 750/2340. Now, add the two fractions: 1796/2340 + 750/234
Expected answer: 47429/11564
Correct? No
Problem: Solve the following two steps: first, subtract 76/30 from 91/16 and second, add the answer to 18/44. Round the final answer to the nearest hundredth.
Mixtral 8x7B:
Step 1: Subtract 76/30 from 91/16. First, convert 91/16 to a common denominator of 120 (the least common multiple of 16 and 30). 91/16 becomes 546/120. Then, subtract 76/30 from 546/120 to get 470/120. Step 2: Add the answer to 18/44. First, convert 18/44 to a common denominator of 120 (the least common multiple of 44 and 120). 18/44 becomes 54/120. Then, add 470/120 to 54/120 to get 524/120. Rounding to the nearest hundredth, the answer is 4.37. ### Answer: 4.37
Expected answer: 9407/2640
Correct? No
Problem: Calculate the result of ((8 / 91) + (49 / 5)) and subtract (32 / 76) from the result. Provide your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, calculate the sum of (8/91) and (49/5): (8/91) + (49/5) = (40/91) + 98/5 = (80/455) + (1960/455) = 2040/455 Then, subtract (32/76) from the sum: 2040/455 - (32/76) = 2040/455 - 160/76 = 2040/455 - 120/55 = 360/55 - 120/55 = 240/55 Simplify the fraction: 240/55 = (8*30)/(5*11) = 8/5 * 30/11 = 24/11 ### Answer: 24/11
Expected answer: 81841/8645
Correct? No
Problem: Calculate the value of ((75 / 45) + (5 / 49)) first. Then add this value with 3 / 58. Provide the answer as a simple fraction.
Mixtral 8x7B:
Reasoning: First, calculate the value of (75 / 45) + (5 / 49). The greatest common divisor (gcd) of 75 and 45 is 15, so (75 / 45) simplifies to (5 / 3). The greatest common divisor (gcd) of 5 and 49 is 1, so (5 / 49) cannot be simplified further. So, (75 / 45) + (5 / 49) = (5 / 3) + (5 / 49). The least common multiple (lcm) of 3 and 49 is 147, so convert (5 / 3) to (145 / 147). So, (5 / 3) + (5 / 49) = (145 / 147) + (5 / 49) = (145 + 15) / 147 = 160 / 147. Now, add 3 / 58 to the result. The least common multiple (lcm) of 147 and 58 is 4062, so convert 160 / 147 to 2720 / 4062 and 3 / 58 to 69 / 4062. So, 160 / 147 + 3 / 58 = 2720 / 4062 + 69 / 4062 = (2720 + 69) / 4062 = 2789 / 4062. ### Answer: 2789 / 4062
Expected answer: 15521/8526
Correct? No
Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.
Mixtral 8x7B:
Reasoning: First, calculate the value of the expression: (43 / 15) - (33 / 95) = (43 \* 95) / (15 \* 95) - (33 \* 15) / (95 \* 15) = 4085 / 1425 - 495 / 1425 = 3590 / 1425 Now, simplify the result to its lowest terms: The greatest common divisor (GCD) of 3590 and 1425 is 25. Divide both the numerator and the denominator by the GCD: 3590 / 25 = 143.6 1425 / 25 = 57 ### Answer: 143.6 / 57 or simplified to lowest terms: 1436 / 570
Expected answer: 718/285
Correct? No
Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.
Mixtral 8x7B:
Reasoning: First, we need to find the value of (78 / 45) + (89 / 36). To do this, find a common denominator for the fractions, which is 1080 (the least common multiple of 45 and 36). (78 / 45) + (89 / 36) = (78 \* 24) / 1080 + (89 \* 30) / 1080 = 1872 / 1080 + 2670 / 1080 = 4542 / 1080 Now, to add this sum to itself, we simply multiply the sum by 2: (4542 / 1080) \* 2 = 9084 / 1080 To simplify the fraction, we need to find the greatest common divisor (GCD) of 9084 and 1080, which is 72. 9084 / 72 = 126 1080 / 72 = 15 So, the simplified fraction is: ### Answer: 126/15
Expected answer: 757/90
Correct? No
Problem: Let's consider that 93 is divided by 34 to get a fraction value, from which is subtracted another fraction 77/74. What would be the result as a simplified fraction?
Mixtral 8x7B:
Reasoning: First, divide 93 by 34 to get the whole number and fraction part: 93/34 = 2 remainder 29. Then, convert the remainder 29 into a fraction by dividing it by the divisor 34: 29/34. Now, subtract the fraction 77/74 from the fraction 29/34: (29-77)/34 = -48/34. Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: -48/34 = -24/17. ### Answer: -24/17
Expected answer: 1066/629
Correct? No
Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 86/35 and 68/85, we need to find a common denominator. The least common multiple of 35 and 85 is 2975. So, we convert 86/35 to have a denominator of 2975: 86/35 \* (2975/2975) = 249750/10725. Similarly, we convert 68/85 to have a denominator of 2975: 68/85 \* (35/35) = 2380/2975. Now, we can add the two fractions: 249750/10725 + 2380/2975 = 249750/10725 + 5233/10725 = 255083/10725. To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator, which is 197. Dividing both the numerator and the denominator by 197, we get: 255083/10725 ÷ 197 = 1295/54. ### Answer: 1295/54
Expected answer: 114/35
Correct? No
Problem: What is the sum of 99/53 and 67/94 in simplest form?
Mixtral 8x7B:
Reasoning: To add the fractions 99/53 and 67/94, we need to find a common denominator. The least common multiple of 53 and 94 is 4902. So, we convert the fractions to have this common denominator: 99/53 = (99 \* 94) / 53 \* 94 = 9207/4902 67/94 = (67 \* 53) / 94 \* 53 = 3511/4902 Now, we can add the fractions: 9207/4902 + 3511/4902 = (9207 + 3511) / 4902 = 12718/4902 Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 12718/4902 = 6359/2451 ### Answer: 6359/2451
Expected answer: 12857/4982
Correct? No
Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?
Mixtral 8x7B:
To find the difference of the two fractions, we first need to get a common denominator. The least common multiple of 27 and 33 is 297. So, we convert 74/27 to 74 \* 11/27 \* 11 = 2744/297 and 56/33 to 56 \* 9/33 \* 9 = 468/297. Now, we can find the difference: 2744/297 - 468/297 = 2276/297. To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 2276 and 297 is 1. Therefore, the simplified form of the fraction is 2276/297. ### Answer: 2276/297
Expected answer: 310/297
Correct? No
Problem: Find the result when you subtract 91/65 from the sum of 96/40 and 11/99. Leave your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, find the sum of 96/40 and 11/99: 96/40 + 11/99 = (96*3 + 11)/132 = 307/132 Then, subtract 91/65 from 307/132: 307/132 - 91/65 = (307*2 - 91*4)/264 = 529/264 Simplify the fraction: 529/264 = 19/11 ### Answer: 19/11
Expected answer: 10/9
Correct? No
Problem: Calculate the sum of the following expressions: 1) Divide 10 by 5 and add that result to 35 divided by 27. This will give you a value h. 2) Then, add 47 divided by 99 to h. This will give you a value p. What is the value of p?
Mixtral 8x7B:
Reasoning: 1) Divide 10 by 5: 10/5 = <<10/5=2>>2. 2) Divide 35 by 27: 35/27 = 1.3 (rounded to two decimal places). 3) Add the results: 2 + 1.3 = <<2+1.3=3.3>>3.3. 4) Divide 47 by 99: 47/99 = 0.474747475 (rounded to ten decimal places). 5) Add the results: 3.3 + 0.474747475 = <<3.3+0.474747475=3.774747475>>3.774747475. ### Answer: 3.774747475
Expected answer: 1120/297
Correct? No
Problem: Consider the fraction 90/81. Add it to 2/66 and simplify your answer to the simplest form. What is the result?
Mixtral 8x7B:
Reasoning: First, we need to convert the fractions to a common denominator. The least common multiple of 81 and 66 is 198. 90/81 = (90 \* 2)/162 = 180/162 2/66 = (2 \* 3)/231 = 6/77 Now, we can add the fractions: 180/162 + 6/77 = (180 \* 77)/(162 \* 77) + (6 \* 162)/(77 \* 162) = 13920/12342 + 972/12342 = 14972/12342 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator: GCD(14972, 12342) = 134 Now, we can divide both the numerator and the denominator by the GCD: 14972 / 134 = 111 12342 / 134 = 92 So, the simplified form of the fraction is 111/92. ### Answer: 111/92
Expected answer: 113/99
Correct? No
Problem: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, how long would both pieces of ribbon be together?
Mixtral 8x7B:
Reasoning: If Oliver gets another piece of ribbon that is the same length as the first piece, then the second piece will also be 56/41 yards long. Together, both pieces of ribbon would be 56/41 + 56/41 = <<56/41+56/41=112/41>>112/41 yards long. ### Answer: 112/41 yards
Expected answer: 112/41
Correct? Yes
Problem: If Oliver receives two more pieces of ribbon, with each being 56/41 yards long, how long would all the pieces of ribbon be when added together?
Mixtral 8x7B:
Reasoning: Oliver already has 2 pieces of ribbon, each 56/4
Expected answer: 224/41
Correct? No
Problem: If Oliver initially had a piece of ribbon that was 63/41 yards long instead of 56/41 yards, and he still receives a second piece of the same length, how long would both pieces of ribbon be when put together?
Mixtral 8x7B:
Reasoning: If Oliver initially had a piece of ribbon that was 63/41 yards long, and then he gets another piece of ribbon that is the same length, then the second piece will also be 63/4
Expected answer: 126/41
Correct? No
Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 92/75 and 66/92, we need to find a common denominator. The common denominator of 75 and 92 is 6420. So, 92/75 = (92 \* 85) / 6420 = 7820 / 6420 And, 66/92 = (66 \* 69) / 6420 = 4534 / 6420 Now, we can add the fractions: 7820 / 6420 + 4534 / 6420 = 12354 / 6420 Simplifying the fraction: 12354 / 6420 = 6617 / 3580 = 3308.5 / 1790 = 19 / 10 + 3 / 10 - 1 / 1790 ### Answer: 19/10 + 3/10 - 1/1790
Expected answer: 6707/3450
Correct? No
Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 32/65 and 73/22, we need to find a common denominator. The least common multiple of 65 and 22 is 1430. So, we convert 32/65 to have a denominator of 1430: 32/65 = (32 \* 22) / 1430 = 704/1430. We convert 73/22 to have a denominator of 1430: 73/22 = (73 \* 65) / 1430 = 4745/1430. Now, we can add the two fractions: 704/1430 + 4745/1430 = 5449/1430. ### Answer: 5449/1430
Expected answer: 5449/1430
Correct? Yes
Problem: Following up on the previous question, what is the sum of your answer from that problem and 24/71? Leave your answer as an unsimplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 5449/1430 and 24/71, we need to find a common denominator. The least common multiple of 1430 and 71 is 101430. So, we convert 5449/1430 to have a denominator of 101430: 5449/1430 = (5449 \* 71) / 101430 = 388809/101430. We convert 24/71 to have a denominator of 101430: 24/71 = (24 \* 1430) / 101430 = 34320/101430. Now, we can add the two fractions: 388809/101430 + 34320/101430 = 423129/101430. ### Answer: 423129/101430 (Note: The fraction 423129/101430 is already in its simplest form, as it cannot be reduced further.)
Expected answer: 421199/101530
Correct? No
Problem: In the earlier problem, we considered the sum of 32/65 and 73/22. But what if the fraction was 53/65 instead of 32/65? What would the new sum be? Please leave your answer as an unsimplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 53/65 and 73/22, we need to find a common denominator. The least common multiple of 65 and 22 is 1430. So, we convert 53/65 to have a denominator of 1430: 53/65 = (53 \* 22) / 1430 = 1166/1430. We convert 73/22 to have a denominator of 1430: 73/22 = (73 \* 65) / 1430 = 4745/1430. Now, we can add the two fractions: 1166/1430 + 4745/1430 = 5911/1430. ### Answer: 5911/1430 (Note: The sum is already in an unsimplified fraction form.)
Expected answer: 5911/1430
Correct? Yes
Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.
Mixtral 8x7B:
Reasoning: To find the difference between two fractions, we first need to find a common denominator. In this case, the common denominator of 34 and 86 is 282 (the least common multiple of 34 and 86). So, we convert 51/34 to have a denominator of 282: 51/34 = (51*8)/(34*8) = 408/272. Similarly, we convert 12/86 to have a denominator of 282: 12/86 = (12*3)/(86*3) = 36/258. Now, we can find the difference: 408/272 - 36/258 = (408*258 - 36*272)/(272*258) = (105888 - 9568)/69936 = 96320/69936. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 16: 96320/16 = 6020 and 69936/16 = 4371. ### Answer: 6020/4371
Expected answer: 117/86
Correct? No
Problem: First take the whole number 51 and add it to the fraction 93/8. Take that sum and add it to the fraction 58/44. What is the final result as a simplified fraction?
Mixtral 8x7B:
Reasoning: First, we need to convert the whole number 51 to a fraction, which is 51/1. Then, we add 51/1 to 93/8. To do this, we need to find a common denominator, which is 8 in this case. So, we convert 51/1 to 408/8 (51*8=408 and 1*8=8) and add it to 93/8 to get 408+93=501/8. Next, we add 501/8 to 58/44. Again, we need to find a common denominator, which is 396 in this case (8*49=392 and 44*9=396). So, we convert 501/8 to 24045/396 (501*49=24045 and 8*49=392) and add it to 58/44 to get 24045+248=24293/396. Finally, we simplify the fraction 24293/396 by dividing both the numerator and the denominator by their greatest common divisor, which is 13. So, we get 24293/396 = 1868/31, which is the final result. ### Answer: 1868/31
Expected answer: 5627/88
Correct? No
Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.
Mixtral 8x7B:
Reasoning: To subtract the fractions, first find a common denominator (the least common multiple of 5 and 25 is 25). Then, convert each fraction to have this common denominator. 82/5 - 98/25 = (82*5)/25 - 98/25 = 410/25 - 98/25 = 312/25 The fraction 312/25 cannot be simplified further, as there are no common factors in the numerator and the denominator. ### Answer: 312/25
Expected answer: 312/25
Correct? Yes
Problem: Given the result you obtained previously from calculating 82/5 - 98/25, what would you get if you added this result to itself?
Mixtral 8x7B:
Reasoning: To add the fraction 312/25 to itself, simply multiply the numerator and the denominator by 2. 312/25 + 312/25 = (312*2)/25 = 624/25 The fraction 624/25 cannot be simplified further, as there are no common factors in the numerator and the denominator. ### Answer: 624/25 (Note: The answer is the same as the result obtained previously, as the subtraction and addition operations cancel each other out.)
Expected answer: 624/25
Correct? Yes
Problem: If you originally had 82/5 oranges and instead of taking away 98/25 of them, you took away 98/90 oranges, how many oranges would you have left? Write the answer in the simplest form.
Mixtral 8x7B:
Reasoning: To subtract the fractions, first find a common denominator (the least common multiple of 5 and 90 is 90). Then, convert each fraction to have this common denominator. 82/5 - 98/90 = 82*18/90 - 98/90 = 1476/90 - 98/90 = 1378/90 The fraction 1378/90 cannot be simplified further, as there are no common factors in the numerator and the denominator. However, we can simplify the answer by dividing both the numerator and the denominator by their greatest common divisor (which is 2). 1378/90 = (1378/2)/(90/2) = 689/45 ### Answer: 689/45 (Note: The answer can be further simplified by dividing both the numerator and the denominator by their greatest common divisor (which is 17), but this is not necessary.)
Expected answer: 689/45
Correct? Yes
Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.
Mixtral 8x7B:
(64 / 50) + (70 / 22) = (64 * 2) / (50 * 2) + (70 * 25) / (22 * 25) = 128 / 100 + 1750 / 550 = 128/100 * 550/550 + 1750/550 * 100/100 = (128 * 550 + 1750 * 100) / (550 * 100) = 70400 + 175000 / 55000 = 245400 / 55000 ### Answer: 245400 / 55000
Expected answer: 1227/275
Correct? Yes
Problem: In the previous question, we considered a situation where we added the fractions (64 / 50) and (70 / 22). Now imagine we made a slight error in our calculations, and the initial fraction was actually (64 / 49), not (64 / 50). How would that affect our total sum? Calculate (64 / 49) + (70 / 22) and provide your answer as an unsimplified fraction.
Mixtral 8x7B:
(64 / 49) + (70 / 22) = (64 * 2) / (49 * 2) + (70 * 25) / (22 * 25) = 128 / 98 + 1750 / 550 = 128/98 * 550/550 + 1750/550 * 98/98 = (128 * 550 + 1750 * 98) / (98 * 550) = 70400 + 171500 / 54900 = 241900 / 54900 ### Answer: 241900 / 54900
Expected answer: 2419/539
Correct? No
Problem: John calculated s by adding 24 divided by 6 to 40 divided by 53. He then added s to itself to get b. Can you find the value of b?
Mixtral 8x7B:
Reasoning: First, we need to find the value of s. s = 24/6 + 40/53 s = 4 + 0.754717 (rounded to 8 decimal places) s ≈ 4.755 (rounded to 3 decimal places) Now, we find the value of b by adding s to itself. b = s + s b = 4.755 + 4.755 b = 9.51 (rounded to 2 decimal places) ### Answer: b ≈ 9.51
Expected answer: 504/53
Correct? No
Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.
Mixtral 8x7B:
Reasoning: First, calculate the two fractions: 80/90 simplifies to 8/9 and 52/11 is already in simplest form. Next, add the two fractions: 8/9 + 52/11 = (8*11 + 52*9) / 99 = 464/99. Finally, convert the improper fraction to a mixed number: 464/99 = 4 71/99. ### Answer: 4 71/99
Expected answer: 556/99
Correct? No
Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 12/18 and 91/74, we first need to find a common denominator. The least common multiple of 18 and 74 is 648. 12/18 = (12 \* 36) / (18 \* 36) = 432 / 648 91/74 = (91 \* 8) / (74 \* 8) = 728 / 592 Now, we can add the numerators and keep the common denominator: (432 + 728) / 648 = 1160 / 648 To simplify the fraction, we need to find the greatest common divisor (GCD) of 1160 and 648. The GCD of 1160 and 648 is 8. 1160 / 8 = 145 648 / 8 = 81 So, the sum of 12/18 and 91/74 is 145/81 as a simplified fraction. ### Answer: 145/81
Expected answer: 421/222
Correct? No
Problem: Find the sum of the fractions 7/2 and 51/25. Write your answer as a simple fraction.
Mixtral 8x7B:
Reasoning: To find the sum of the fractions, we first need to convert them to have a common denominator. The least common multiple of 2 and 25 is 50. 7/2 can be written as 175/50 and 51/25 can be written as 102/50. Now, we can add the fractions: 175/50 + 102/50 = (175 + 102)/50 = 277/50. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 277 ÷ 2 = 138.5 and 50 ÷ 2 = 25. ### Answer: 138.5/25 or 5.55 (rounded to two decimal places)
Expected answer: 277/50
Correct? No
Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.
Mixtral 8x7B:
First, let's calculate the value of the expression ((68 / 69) + (93 / 7)): Change the second fraction to have a common denominator with the first fraction: (93 / 7) = (93 * 69) / (7 * 69) = 6381 / 483 Now, add the fractions: (68 / 69) + (6381 / 483) = (68 * 483) / (69 * 483) + (6381 * 69) / (483 * 69) = 32864 / 32867 Now, add this result to (3 / 46): (32864 / 32867) + (3 / 46) = (32864 * 46) / (32867 * 46) + (3 * 32867) / (46 * 32867) = 1524568 / 1402462 So, the resulting value as a simple fraction is 1524568 / 1402462.
Expected answer: 13849/966
Correct? No
Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 98 and 4 is 98, so we convert 60/4 to 14\*60/4\*98 = 2100/2352. Then, we add the fractions: 31/98 + 2100/2352 = (31\*2352 + 2100\*98)/(98\*2352) = 74928/229952. To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 8: 74928/229952 = 9366/28744. ### Answer: 9366/28744
Expected answer: 1501/98
Correct? No
Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we simplify the fractions 3/2 and 24/36 to their lowest terms, which are 1 1/2 and 2/3, respectively. Then, we add the fractions: 1 1/2 + 2/3 = (3/2 + 2/3) = (3*3 + 2*2)/(2*3) = 11/6. ### Answer: 11/6
Expected answer: 13/6
Correct? No
Problem: Firstly, calculate the sum of 92/54 and 90/13, then from the result take away 46/41. What's the result as a simplified fraction?
Mixtral 8x7B:
Reasoning: First, we need to convert the fractions so they have a common denominator. The least common multiple of 54 and 13 is 669, so we get: 92/54 = (92 \* 12)/(54 \* 12) = 1104/648 90/13 = (90 \* 51)/(13 \* 51) = 4590/669 Now, we can add these two fractions: 1104/648 + 4590/669 = (1104 \* 669 + 4590 \* 648)/(648 \* 669) = 1238520/439992 Next, we subtract 46/41 from this result: (1238520/439992) - (46/41) = (1238520 \* 41 - 46 \* 439992)/(439992 \* 41) = (50946320 - 20159712)/18179712 = 30786608/18179712 Finally, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8: 30786608/18179712 = (30786608/8) / (18179712/8) = 3848326/2272464 Again, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8: 3848326/2272464 = (3848326/8) / (2272464/8) = 481040.75/284058 Again, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 481040.75/284058 = (481040.75/2) / (284058/2) = 240520.375/142029 Again, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1: 240520.375/142029 = 240520.375/142029 Since this fraction cannot be simplified further, this is the final answer. ### Answer: 240520.375/142029
Expected answer: 108002/14391
Correct? No
Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.
Mixtral 8x7B:
Twice the value of 29/23 is 2*(29/23) = <<2*29/23=58/23=2 9/23>>2 9/23. This fraction cannot be simplified further because 29 and 23 are both prime numbers and do not share any common factors other than 1. ### Answer: 2 9/23
Expected answer: 58/23
Correct? No
Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need a common denominator. The least common multiple of 20 and 72 is 20*3*6 = 360. So, convert 29/20 to 29*18/20*18 = 513/360 and 17/72 to 17*5/72*5 = 85/360. Then, add the fractions: 513/360 + 85/360 = (513+85)/360 = 598/360. Simplify the fraction: 598/360 = 299/180. ### Answer: 299/180
Expected answer: 607/360
Correct? No
Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.
Mixtral 8x7B:
Reasoning: First, we simplify the expression inside the parentheses. 36 / 27 simplifies to 1.
Expected answer: 1993/237
Correct? No
Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of (86 / 71) and (91 / 75) as decimals. (86 / 71) ≈ 1.21126761 (91 / 75) ≈ 1.21333333 Then, we add these two decimals: 1.21126761 + 1.21333333 ≈ 2.4246 Finally, we need to round this decimal to the nearest hundredth, which is 2.42. ### Answer: 2.42
Expected answer: 12911/5325
Correct? No
Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)
Mixtral 8x7B:
Reasoning: First, convert each term to a common denominator (the least common multiple of 75, 43, and 62 is 18090): (21 * 234) / (75 * 234) + (74 * 420) / (43 * 420) + (10 * 285) / (62 * 285) Simplify each term: 4917 / 17550 + 3088 / 18260 + 2850 / 17490 Now, add the fractions: (4917 * 18260 + 3088 * 17550 + 2850 * 18260) / 17550 * 18260 Simplify the numerator: 89522660 + 53846840 + 52105500 = 195474900 The simplified fraction is: 195474900 / (17550 * 18260) Further simplify the fraction: 195474900 / 3189949100 = 6763 / 112570 ### Answer: 6763 / 112570
Expected answer: 72056/33325
Correct? No
Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.
Mixtral 8x7B:
Reasoning: First, we perform the division operations inside the parentheses: (1.136363636... + 1.327868852...). Then, we add the results: 2.464232488... To reduce this decimal number to a fraction, we need to determine the common denominator of 66 and 61, which is 66 \* 61 = 4026. We convert the decimal number to a fraction by multiplying both the numerator and the denominator by a power of 10 to make the numerator a whole number: 2.464232488... \* 10000 = 24642.32488... / 10000 = 24642 / 10000. Now, we convert the numerator to an equivalent value with the common denominator: 24642 = 24642 \* (61 / 61) = (24642 \* 61) / 61 = 1506306 / 61. So, the final answer is: ### Answer: 1506306 / 61000
Expected answer: 3307/1342
Correct? No
Problem: Consider two identical fractions, t, each equal to sum of 53/18 and 21/99. Find the total sum, l, of these fractions and present your answer as a simple fraction.
Mixtral 8x7B:
Since the two fractions are identical, we only need to find the value of one of them. t = 53/18 + 21/99 To add fractions, we need to have the same denominator. The least common denominator of 18 and 99 is 198. t = (53 \* 11)/198 + (21 \* 2)/198 t = 583/198 + 42/198 t = (583 + 42)/198 t = 625/198 Since both fractions are identical, l = t + t = 2t l = 2 \* (625/198) ### Answer: l = 1250/198
Expected answer: 625/99
Correct? Yes
Problem: Consider the previous situation where you calculated the sum of two identical fractions, t, both equal to the sum of 53/18 and 21/99. You found the total sum, l. Now, add the fraction 99/92 to l, and call this total c. What is c expressed as a simplified fraction?
Mixtral 8x7B:
We have already found that t = 625/198 and l = 2t = 1250/198. Now, we need to find c = l + 99/92 First, we need to have the same denominator for the fractions in c. The least common denominator of 198 and 92 is 9504. c = (1250 \* 48)/9504 + (99 \* 99)/9504 c = 59600/9504 + 9801/9504 c = (59600 + 9801)/9504 c = 69401/9504 Now, we need to simplify the fraction c. The greatest common divisor of 69401 and 9504 is 1. Therefore, c = 69401/9504 is already in its simplest form. ### Answer: c = 69401/9504
Expected answer: 67301/9108
Correct? No
Problem: Remember the earlier situation where you found the sum of two identical fractions, each equal to the sum of 53/18 and 21/99. Now, suppose that each fraction was instead equal to the sum of 76/18 and 21/99. You add these two identical fractions together to get a new total, which we will call w. What is w expressed as a simple fraction?
Mixtral 8x7B:
Reasoning: Let's first find the value of one of the identical fractions. f = 76/18 + 21/99 To add fractions, we need to have the same denominator. The least common denominator of 18 and 99 is 198. f = (76 \* 11)/198 + (21 \* 2)/198 f = 836/198 + 42/198 f = (836 + 42)/198 f = 878/198 Since both fractions are identical, w = f + f = 2f w = 2 \* (878/198) ### Answer: w = 1756/198 or w = 439/49 (simplified)
Expected answer: 878/99
Correct? Yes
Problem: First, calculate the result of 58/49 + 31/34. Then, add that result to the fraction 74/38. What is the final result as a simple fraction?
Mixtral 8x7B:
First, calculate the result of 58/49 + 31/34. To do this, find a common denominator for 49 and 34. The least common multiple of 49 and 34 is 1614. 58/49 = (58 \* 33)/(49 \* 33) = 1904/1614 31/34 = (31 \* 46)/(34 \* 46) = 1426/1564 Now, add the two fractions: 1904/1614 + 1426/1
Expected answer: 127971/31654
Correct? No
Problem: Calculate the sum of 100 divided by 76 and 29 divided by 14. Please provide your answer as a simplified fraction or decimal.
Mixtral 8x7B:
Reasoning: To add the two fractions, we first need to find a common denominator. The least common multiple of 76 and 14 is 308. Then, we convert the fractions to have this common denominator: 100/76 = (100*4)/(76*4) = 400/304 29/14 = (29*22)/(14*22) = 638/308 Now, we can add the fractions: 400/304 + 638/308 = (400+638)/308 = 1038/308 This fraction cannot be simplified further, so we will leave it as is. ### Answer: 1038/308 or approximately 3.367 (rounded to 4 decimal places)
Expected answer: 901/266
Correct? No
Problem: Given that Evan has read 51/18 of his novel, and Olivia has read (8/42) after reading the same amount of novel as Evan, how much of the novel has Olivia read in total? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: Olivia has read the same amount as Evan, which is 51/18 of the novel. Olivia's portion is (51/18) * (8/42) = (51 * 8) / (18 * 42) = 408 / 756 = 136 / 252 = 34 / 63. ### Answer: 34/63
Expected answer: 127/42
Correct? No
Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.
Mixtral 8x7B:
Reasoning: The sum of 48/13 and 31/22 can be calculated by finding a common denominator for 13 and 22, which is 13*22 = 286. Then, convert 48/13 to 48*22/13*22 = 1076/286 and 31/22 to 31*13/22*13 = 403/286. Now, add 1076/286 + 403/286 = 1479/286. ### Answer: 1479/286 (as a simplified fraction) or 5.1716 (as a decimal)
Expected answer: 1459/286
Correct? No
Problem: First, find the value of 24/86 + 76/77. Subtract your answer from 27/6. Write out your process and show your work.
Mixtral 8x7B:
Reasoning: First, we need to convert the mixed number 27/6 to an improper fraction, which is (27*1)/6 = 27/6 = 4 3/6 = 4 1/2. Next, we calculate the value of 24/86 + 76/77. To do this, we need a common denominator, which is 86*77 = 6622. So, 24/86 = (24*77)/6622 = 1872/6622 and 76/77 = (76*86)/6622 = 6556/6622. Therefore, 24/86 + 76/77 = 1872/6622 + 6556/662
Expected answer: 21415/6622
Correct? No
Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 73/39 and 49/14, we first find a common denominator, which is
Expected answer: 419/78
Correct? No
Problem: What is the sum of 75/65 and 7/39? Simplify your answer.
Mixtral 8x7B:
Reasoning: To add the fractions 75/65 and 7/39, we need to get them over a common denominator. The least common multiple of 65 and 39 is 2610. So, we convert the fractions to have this common denominator: 75/65 = (75 \* 41) / (65 \* 41) = 3075 / 2665 7/39 = (7 \* 68) / (39 \* 68) = 476 / 2665 Now, we can add the fractions: 3075 / 2665 + 476 / 2665 = (3075 + 476) / 2665 = 3551 / 2665 The fraction 3551/2665 cannot be simplified further, so this is the final answer. ### Answer: 3551/2665
Expected answer: 4/3
Correct? No
Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?
Mixtral 8x7B:
Reasoning: First, calculate the value of 79/1 - 30/92. To do this, find a common denominator for 1 and 92. The least common multiple of 1 and 92 is 92. 79/1 - 30/92 = 79 - 30/92 = 79 - 3/92 = 78.875 Next, subtract 61/63 from the result. To do this, find a common denominator for 92 and 63. The least common multiple of 92 and 63 is 2016. 78.875 \* (2016/2016) - 61/63 \* (33/33) = 15942.5/2016 - 2003/2016 = 13939.5/2016 ### Answer: 13939.5/2016 or approximately 6.917 (rounded to 4 decimal places)
Expected answer: 225191/2898
Correct? No
Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.
Mixtral 8x7B:
Reasoning: (58 / 26) + (58 / 26) = 1 + 1 = 2. Since 26 is a factor of 58, the fraction 58/26 can be simplified to 2/1, which is already in its simplest form. ### Answer: 2 + 2 = 4 or 4/1 in simplest form.
Expected answer: 58/13
Correct? No
Problem: If Alex has 69/63 gallons of orange juice and he bought additional 77/5 gallons, giving him a total of 'k' gallons. Later, he received another 47/71 gallons of orange juice from Sally. How many gallons did Alex have in total?
Mixtral 8x7B:
First, we need to find out how many gallons of orange juice Alex had after buying the additional 77/5 gallons. To do this, we add the 69/63 gallons he already had to the 77/5 gallons he bought: (69/63 + 77/5) = (69/63 \* 5/5 + 77/5 \* 63/63) = (345/315 + 4809/315) = 5154/315 gallons Then, we add the 47/71 gallons he received from Sally: 5154/315 + 47/71 = (5154 \* 71/315 + 47 \* 45/71) / (71 \* 5/71) = (367108/2205 + 2115/71) / 5 = (367108 + 30015)/(5 \* 2205) = 397123/11025 gallons ### Answer: Alex had 397123/11025 gallons of orange juice in total.
Expected answer: 127907/7455
Correct? No
Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (1.64 (rounded to two decimal places) + (6.5 + 1.37)) Then, perform the addition operations: 1.64 + 7.87 = 9.51 Since the question asks for the answer as a simplified fraction, convert the decimal number to a fraction: 9.51 = 951/100 ### Answer: 951/100
Expected answer: 56831/5978
Correct? No
Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.
Mixtral 8x7B:
Reasoning: To add the fractions, we need a common denominator. The least common multiple of 1 and 69 is 69. So, we convert 85/1 to have a denominator of 69: 85/1 x 69/69 = 5885/69. Now, we can add the fractions: 83/69 + 5885/69 = 5968/69. The fraction 5968/69 cannot be simplified any further. ### Answer: 5968/69
Expected answer: 5948/69
Correct? No
Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?
Mixtral 8x7B:
Reasoning: The least common multiple of the denominators 13 and 86 is 1066. So, convert each fraction to an equivalent fraction with denominator 1066. 92/13 - (92 \* 86) / (13 \* 86) = 92/1
Expected answer: 197/26
Correct? No
Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?
Mixtral 8x7B:
Reasoning: To add the fractions, we need a common denominator. The least common multiple of 32 and 98 is 3024. So, we convert 67/32 to 67 \* 3024/3024 / 32 = 60432/101344 and 10/98 to 10 \* 15/15 / 98 = 150/14112. Then, we add the fractions: 60432/101344 + 150/14112 = 61942/101344. Finally, we simplify the fraction: 61942/101344 = 30971/50672. ### Answer: 30971/50672
Expected answer: 3443/1568
Correct? No
Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 59/52 and 70/32, we need to find a common denominator. The common denominator of 52 and 32 is 16 * 52 = <<16*52=832>>832. So, 59/52 = (59 * 16) / 832 = 944 / 832 and 70/32 = (70 * 26) / 832 = 1820 / 832. Now, we can add the fractions: 944 / 832 + 1820 / 832 = (944 + 1820) / 832 = 2764 / 832. The fraction 2764 / 832 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 2764 / 832 = (2764 / 4) / (832 / 4) = 691 / 208. ### Answer: 691/208
Expected answer: 691/208
Correct? Yes
Problem: After finding the sum of 59/52 and 70/32, add this to 42/41. What is the final sum as a simplified fraction?
Mixtral 8x7B:
Reasoning: We first found the sum of 59/52 and 70/32, which is 691/208. Now, we need to add this sum to 42/41. To add the fractions 691/208 and 42/41, we need to find a common denominator. The common denominator of 208 and 41 is 208 * 41 = <<208*41=8568>>8568. So, 691/208 = (691 * 41) / 8568 = 28491 / 8568 and 42/41 = (42 * 208) / 8568 = 8736 / 8568. Now, we can add the fractions: 28491 / 8568 + 8736 / 8568 = (28491 + 8736) / 8568 = 37227 / 8568. The fraction 37227 / 8568 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 9: 37227 / 8568 = (37227 / 9) / (8568 / 9) = 4136.33 / 952. ### Answer: 4136.33/952 (Note: The answer is expressed as a fraction, but it can also be expressed as a decimal number.)
Expected answer: 37067/8528
Correct? No
Problem: After recalculating the original problem with 74/52 instead of 59/52 and still adding this to 70/32, what is the new sum as a simplified fraction?
Mixtral 8x7B:
Reasoning: To add the fractions 74/52 and 70/32, we need to find a common denominator. The common denominator of 52 and 32 is 16 \* 52 = <<16*52=832>>832. So, 74/52 = (74 \* 16) / 832 = 1184 / 832 and 70/32 = (70 \* 26) / 832 = 1820 / 832. Now, we can add the fractions: 1184 / 832 + 1820 / 832 = (1184 + 1820) / 832 = 3004 / 832. The fraction 3004 / 832 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 3004 / 832 = (3004 / 4) / (832 / 4) = 751 / 208. ### Answer: 751/208 (Note: This answer is different from the previous one because the numerator of the first fraction has changed from 59 to 74.)
Expected answer: 751/208
Correct? Yes
Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?
Mixtral 8x7B:
Reasoning: First, perform the division operations: 48/5 = <<48/5=9.6>>9.6 and 11/65 = <<11/65=0.16923076923076923>>0.1692 (rounded to two decimal places). Then, subtract 48/5 from 11/65: 0.1692 - 9.6 = -9.4308 (rounded to four decimal places). Finally, add the result to 28/2: -9.4308 + 28/2 = -9.4308 + 14 = <<-9.4308+14=4.5692>>4.5692. ### Answer: 4.5692
Expected answer: 1523/65
Correct? No
Problem: What is the result when you add 20/52 to 75/82? Simplify your answer to the smallest possible fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 20/52 and 75/82, we need to find a common denominator. The least common multiple of 52 and 82 is 4204. So, convert 20/52 to 416/4204 and 75/82 to 897/4204. Then, add the fractions: 416/4204 + 897/4204 = 1313/4204. Simplify the fraction: 1313/4204 = 164/526. ### Answer: 164/526
Expected answer: 1385/1066
Correct? No
Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To subtract two fractions, we need to get a common denominator. In this case, the common denominator of 84 and 5 is 420. So, we convert 31/5 to 31 \* 84/5 \* 84 = 22104/5 = 5526/125. And we convert 92/84 to 92 \* 125/84 \* 125 = 115000/105125. Now, we can subtract: 5526/1
Expected answer: 536/105
Correct? No
Problem: Calculate the following: Double the sum of 81/90 and 94/49.
Mixtral 8x7B:
Reasoning: First, find the sum of 81/90 and
Expected answer: 1381/245
Correct? No
Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.
Mixtral 8x7B:
Reasoning: To find the difference between 69/21 and 10/92, we first need to get them over a common denominator. The least common multiple of 21 and 92 is 588 (21*28 and 92*6). So, we convert 69/21 to have a denominator of 588 by multiplying both the numerator and denominator by 28: 69/21 * (28/28) = 1912/588 We convert 10/92 to have a denominator of 588 by multiplying both the numerator and denominator by 6: 10/92 * (6/6) = 60/588 Now, we can find the difference: 1912/588 - 60/588 = (1912-60)/588 = 1852/588 Finally, we simplify the fraction: 1852/588 = 463/147 ### Answer: 463/147
Expected answer: 1023/322
Correct? No
Problem: First, find the result of (26 / 87) + (92 / 88). Then add the result to (26 / 57). What's the answer?
Mixtral 8x7B:
Reasoning: First, find the results of the two separate expressions: (26 / 87) + (92 / 88) and (26 / 57). (26 / 87) + (92 / 88) = 0.3034 + 1.0455 = 1.3489 Then, add this result to (26 / 57): 1.3489 + (26 / 57) = 1.3489 + 0.4561 = 1.8050 ### Answer: 1.8050
Expected answer: 21825/12122
Correct? No
Problem: What is the result if you add 78/66, 28/6, and 90/34 together? Please provide your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, find the common denominator of 66, 6, and 34, which is 204. Then, convert each fraction to have this common denominator. 78/66 becomes (78 \* 3)/204 = 234/204, which simplifies to 1 1/3. 28/6 becomes (28 \* 34)/204 = 952/204, which simplifies to 4 23/51. 90/34 becomes (90 \* 6)/204 = 540/204, which simplifies to 15/6. Now, add the simplified fractions: 1 1/3 + 4 23/51 + 15/6. To add the fractions, first convert 1 1/3 to 4/3 and 15/6 to 5/2. Now, add the fractions: 4/3 + 4 23/51 + 5/2. The least common denominator is 102, so convert the fractions: 8/102 + 260/102 + 255/102. Now, add the fractions: 573/102, which simplifies to 1 53/102. ### Answer: 1 53/102.
Expected answer: 4766/561
Correct? No
Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.
Mixtral 8x7B:
Reasoning: First, we perform the division operations: (12 / 7) - (9 / 23) = 1.71428571 - 0.391304348 = 1.322981362 To simplify the result to the lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator of the result: GCD(1322981362, 10000000) = 1964614 Now, we divide both the numerator and the denominator by the GCD: 1322981362 / 1964614 = 673 10000000 / 1964614 ≈ 5.087 So, the simplified result is: ### Answer: 673/5 Note: The result cannot be expressed as a fraction with integer numerator and denominator, so it is left as a fraction in the lowest terms.
Expected answer: 213/161
Correct? No
Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To find the sum of 95/18 and 51/61, we first need to find a common denominator. The least common multiple of 18 and 61 is 1098. So, convert 95/18 to 95*(61)/(18*61) = 5745/1102 and convert 51/61 to 51*(18)/(61*18) = 918/1102. Now, add the two fractions: 5745/1102 + 918/1102 = (5745+918)/1102 = 6663/1102. Simplify the fraction: 6663/1102 = 21*317/2*5*53 = 63/10. ### Answer: 63/10
Expected answer: 6713/1098
Correct? No
Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, get a common denominator for the fractions by multiplying the two denominators together: 46 \* 84 = 3864. Then, convert the fractions to have this common denominator: (93 \* 84) / 3864 and (51 \* 46) / 3864. This simplifies to (7884 / 3864) - (2376 / 3864). Now, subtract the numerators: 7884 - 2376 = 5508 / 3864. Finally, simplify the fraction: 5508 / 3864 = 225 / 162 = 75 / 54 = 25 / 18. ### Answer: 25 / 18
Expected answer: 911/644
Correct? No
Problem: Calculate the sum of the fractions 12/70 and 84/9. Please provide your answer in simplified form.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. In this case, the least common multiple of 70 and 9 is 630. So, we convert each fraction to have this denominator: 12/70 = (12 \* 9) / 630 = 108/630 84/9 = (84 \* 70) / 630 = 5880/630 Now, we can add the fractions: 108/630 + 5880/630 = 5988/630 Finally, we simplify the fraction: 5988/630 = 854/90 ### Answer: 854/90
Expected answer: 998/105
Correct? No
Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?
Mixtral 8x7B:
Reasoning: First, we need to subtract 40/92 from 32/3. To do this, we need a common denominator, which is 92 * 3 = <<92*3=276>>276. So, 32/3 becomes (32 * 32) / 276 = 320 / 276 and 40/92 becomes 40 / 276. Now, we can subtract 40 / 276 from 320 / 276, which is (320 - 40) / 276 = 280 / 276. Doubling this result gives us 2 * 280 / 276 = 560 / 276, which simplifies to 56 / 34. ### Answer: 56 / 34 or 16 / 17 (when simplified)
Expected answer: 1412/69
Correct? No
Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: The sum of 79/24 and 79/24 is 79/24 + 79/24 = (79+79)/24 = 158/24. The fraction 158/24 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 158/24 = 79/12. ### Answer: 79/12
Expected answer: 79/12
Correct? Yes
Problem: In continuation to the previous problem, now find out what is the sum of two times the previously found sum. In other words, calculate (79/24 + 79/24) + (79/24 + 79/24). Please answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: The sum of (79/24 + 79/24) + (79/24 + 79/24) is 79/12 + 79/12 = (79+79)/12 = 158/12. The fraction 158/12 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 158/12 = 79/6. ### Answer: 79/6 (Note: This answer is equivalent to the answer of the previous problem multiplied by 2.)
Expected answer: 79/6
Correct? Yes
Problem: In the previous problem, you added together two fractions of 79/24. Now, consider if those were fractions of 79/20 instead. What would be the total if you added together two fractions of 79/20? Please express your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: The sum of 79/20 and 79/20 is 79/20 + 79/20 = (79+79)/20 = 158/20. The fraction 158/20 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 158/20 = 79/10. ### Answer: 79/10
Expected answer: 79/10
Correct? Yes
Problem: What is the sum of 91/76 and 12/22? Please simplify your fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 76 and 22 is 184. So, we convert each fraction to have this denominator: 91/76 = (91 \* 2) / 152 = 182/152 12/22 = (12 \* 7) / 154 = 84/154 Now, we can add the fractions: 182/152 + 84/154 = (182 \* 154 + 84 \* 152) / (152 \* 154) = 28092/23648 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 28092 and 23648 is 1056. So, we divide both the numerator and the denominator by the GCD: 28092 / 1056 = 26.666... and 23648 / 1056 = 22.444... ### Answer: The sum of 91/76 and 12/22 is 26.666... (repeating), or in simplified form, 28092/23648.
Expected answer: 1457/836
Correct? No
Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?
Mixtral 8x7B:
Reasoning: First, add 88/93 and 6/47. To do this, find a common denominator, which is 4001 in this case. Then, 88/93 becomes (88*47)/4001 = 4136/4001 and 6/47 becomes (6*93)/4001 = 558/4001. Adding these two fractions gives (4136+558)/40
Expected answer: 105227/4371
Correct? No
Problem: Calculate the sum of 95/83 and the result of 52/21 + 75/67. Write your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of 52/21 + 75/67. To do this, we need a common denominator, which is
Expected answer: 553562/116781
Correct? No
Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, calculate the value of each fraction separately: 73 / 27 = 2.6923076923076923 (rounded to 15 decimal places) 23 / 48 = 0.47916666666666667 (rounded to 15 decimal places) Now, subtract the two values: 2.6923076923076923 - 0.47916666666666667 = 2.213141025641025 (rounded to 15 decimal places) Finally, convert the decimal number to a fraction: 2.213141025641025 = 2 10/87 (simplified) ### Answer: 2 10/87
Expected answer: 961/432
Correct? No
Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.
Mixtral 8x7B:
Reasoning: First, perform the division operations: 78 / 2 = 39 70 / 23 ≈ 3.0435 Then, subtract: 39 - 3.0435 ≈ 35.9565 Since the result is a decimal number, there is no need to simplify it further. ### Answer: 35.9565 (as a decimal) or 35 27/32 (as a fraction)
Expected answer: 827/23
Correct? No
Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.
Mixtral 8x7B:
First, find a common denominator for the fractions 34/1 and 53/4. The least common multiple of 1 and 4 is 4. So, convert 34/1 to have a denominator of 4: 34/1 * 4/4 = 136/4. Now, add the fractions: 136/4 + 53/4 = (136 + 53)/4 = 189/4. Convert 189/4 to a mixed number: 189/4 = 47 remainder 1, so 189/4 = 47 1/4. ### Answer: 47 1/4
Expected answer: 189/4
Correct? Yes
Problem: Following the result of the previous problem, what is the sum of 24/67 and the result you got from adding 34/1 to 53/4? Express your answer as a mixed number.
Mixtral 8x7B:
The result of adding 34/1 to 53/4 is 189/4. Now, add 24/67 to 189/4. First, find a common denominator for the fractions 24/67 and 189/4. The least common multiple of 67 and 4 is 268. So, convert 24/67 to have a denominator of 268: 24/67 * 4/4 = 96/268. Convert 189/4 to have a denominator of 268: 189/4 * 67/67 = 12633/268. Now, add the fractions: 96/268 + 12633/268 = (96 + 12633)/268 = 12729/268. Convert 12729/268 to a mixed number: 12729/268 = 47 remainder 111, so 12729/268 = 47 111/268. ### Answer: 47 111/268 (Note: The fractional part of the answer is greater than 1, so the answer is a mixed number with a whole number part of 47 and a fractional part of 111/268.)
Expected answer: 12759/268
Correct? No
Problem: Let's reconsider the problem where you were adding fractions. Previously, it was asked to add 34/1 to 53/4. Now consider whether it may have been 34/97 instead of 34/1. What will be the result if you add 34/97 to 53/4? Write your answer as a mixed number.
Mixtral 8x7B:
First, find a common denominator for the fractions 34/97 and 53/4. The least common multiple of 97 and 4 is 388. So, convert 53/4 to have a denominator of 388: 53/4 * 97/97 = 5151/388. Now, add the fractions: 34/97 + 5151/388 = (34 \* 4 + 5151)/388 = 5185/388. Convert 5185/388 to a mixed number: 5185/388 = 13 remainder 207, so 5185/388 = 13 207/388. Since 207 is greater than 388, divide 207 by 388 to get a quotient and remainder: 207/388 = 0 remainder 207. So, 5185/388 = 13 + 0 + 207/388 = 13 0 207/388. ### Answer: 13 0 207/388
Expected answer: 5277/388
Correct? No
Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 3/36 and 97/96, we need to get them over a common denominator. The least common multiple of 36 and 96 is 144, so we convert both fractions to have this denominator. 3/36 = (3 \* 4)/(36 \* 4) = 12/144 97/96 = (97 \* 1)/(96 \* 1) = 97/96 Now we can add the fractions: 12/144 + 97/96 = (12 + (97 \* 1))/144 = 109/144 ### Answer: 109/144
Expected answer: 35/32
Correct? No
Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: Calculate the terms in the parentheses first: 92/95 can't be simplified further, and 4/74 simplifies to 1/18. So, the expression becomes: (92/95) + (1/18). To add the fractions, find a common denominator, which is 1710 (the least common multiple of 95 and 18). Convert each fraction to have this common denominator: (92 \* 18) / 1710 + (1 \* 95) / 1710 = 1656 / 1710 + 95 / 1710 Now, add the fractions: (1656 + 95) / 1710 = 1751 / 1710 The fraction 1751/1710 can't be simplified further, as there is no common factor for 1751 and 1710 other than 1. ### Answer: 1751/1710
Expected answer: 3594/3515
Correct? No
Problem: If the value of a variable 'v' is 69/47, what is the value of 'd' if 'd' equals 88/72 + 'v'? Please write your answer as a fraction.
Mixtral 8x7B:
Reasoning: First, we need to find the value of 'v' which is 69/47. Then, we need to find the value of 88/72 + 69/47. To add the fractions, we need to find a common denominator. The least common multiple of 72 and 47 is 3504. So, we convert 88/72 to 2496/3504 and 69/47 to 1452/3504. Then, we add the fractions: 2496/3504 + 1452/3504 = 3948/3504. We simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor of 3948 and 3504, which is 12. 3948 ÷ 12 = 329 and 3504 ÷ 12 = 292. ### Answer: d = 329/292
Expected answer: 1138/423
Correct? No
Problem: Let's say there is a wholesaler who has 41/26 barrels of olive oil in their warehouse. They sell a portion of the oil which is equivalent to 41/72 barrels. How much olive oil do they have now? Express your answer as a simple fraction.
Mixtral 8x7B:
Reasoning: The wholesaler sold 41/72 barrels, so they have 41/26 - 41/72 = (84-41)/72 = 43/72 barrels left. ### Answer: 43/72 (as a simplified fraction)
Expected answer: 943/936
Correct? No
Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.
Mixtral 8x7B:
Reasoning: To find the sum of 85/75 and 88/56, we first need to find a common denominator. The least common multiple of 75 and 56 is 2520. So, we convert 85/75 to 85*32/75*32 = 2816/2400 and 88/56 to 88*45/56*45 = 3792/2520. Then, we add the two fractions: 2816/2400 + 3792/2520 = 6608/4920. Finally, we simplify the fraction to get the sum in decimal form: 6608/4920 = 1.34265... ≈ 1.34. ### Answer: 1.34
Expected answer: 284/105
Correct? No
Problem: What is the result of adding 12 over 33 to 49 over 2? Write your answer as a mixed fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 12/33 and 49/2, we first need to get a common denominator. The least common multiple of 33 and 2 is 66, so we convert 49/2 to 147/66. Then, we add the fractions: 12/33 + 147/66 = (12 + 147)/66 = 159/66. To convert the improper fraction 159/66 to a mixed fraction, we divide 159 by 66 to get a quotient of 2 and a remainder of 33. ### Answer: 2 33/66 (or simplified: 2 1/2)
Expected answer: 547/22
Correct? No
Problem: What is the result of adding two fractions, where each fraction is 78/65?
Mixtral 8x7B:
Since both fractions are identical, you can simply double the value of one fraction to find the sum. ### Answer: 78/65 + 78/65 = (2 * 78) / 65 = 156 / 65 = <<156/65=2.4>>2.4
Expected answer: 12/5
Correct? Yes
Problem: After obtaining the result from the previous problem, where you added two fractions both equal to 78/65, what would you get if you add the result to 71/32?
Mixtral 8x7B:
First, we need to find a common denominator for the fraction 71/32. The least common multiple of 32 and 65 is 208. We convert 78/65 to have a denominator of 208 by multiplying both the numerator and denominator by 3: (78 \* 3) / (65 \* 3) = 234 / 195 Now, we can add the two fractions: 234 / 195 + 71 / 32 To add the fractions, we need to find a common denominator, which is 195 \* 2 = 390. We convert 71 / 32 to have a denominator of 390 by multiplying both the numerator and denominator by 12: (71 \* 12) / (32 \* 12) = 852 / 384 Now, we can add the two fractions: 234 / 195 + 852 / 384 Since the denominators are the same, we can add the numerators: 234 + 852 = 1086 The final answer is 1086 / 390, which simplifies to 362 / 130. ### Answer: 362 / 130 or approximately 2.785 when rounded to four decimal places.
Expected answer: 739/160
Correct? No
Problem: Suppose that instead of having two fractions both equal to 78/65 like in the previous problem, they were both equal to 78/78. What would be the result of adding these two fractions together?
Mixtral 8x7B:
Since both fractions are identical and equal to 1, you can simply add the values to find the sum. ### Answer: 78/78 + 78/78 = 1 + 1 = 2 (Note that 78/78 is equivalent to 1, as any number divided by itself equals 1.)
Expected answer: 2
Correct? No
Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 16/7 and 11/90, we need to have a common denominator. The least common multiple of 7 and 90 is 630. So, we convert 16/7 to 16*90/7*90 = 1440/630 and 11/90 to 11*7/90*7 = 77/630. Then, we add the two fractions: 1440/630 + 77/630 = 1517/630. Finally, we simplify the fraction: 1517/630 = 1009/420. ### Answer: 1009/420
Expected answer: 1517/630
Correct? No